Abstract:We present an analysis of atmospheric neutrino data from a 33.0 kton yr (535-day) exposure of the Super-Kamiokande detector. The data exhibit a zenith angle dependent deficit of muon neutrinos which is inconsistent with expectations based on calculations of the atmospheric neutrino flux. Experimental biases and uncertainties in the prediction of neutrino fluxes and cross sections are unable to explain our observation. The data are consistent, however, with two-flavor νμ ↔ ντ oscillations with sin2 2θ > 0.82 and 5 × 10-4 < Δm2 < 6 × 10-3 eV2 at 90% confidence level.